A study on the qualitative properties for effects of two delays on dynamical behaviors of HIV-AIDS-TB model

In order to simulate the co-infection of AIDS, HIV, and tuberculosis, a time-delay epidemic model is presented in this study. We investigate the effects of delay on mathematical models of AIDS, HIV, and tuberculosis. The suggested system is divided into four classes: AIDS patients, TB infectives, HIV infectives (with or without TB), and susceptibles. The model shows four equilibrium states: endemic, HIV-, TB-, and disease-free. Even though positive endemic equilibrium is always locally stable, there are circumstances in which it might turn into globally stable, indicating that the disease has spread beyond. Delay(which is incorporated in TB infectives and HIV infectives) analysis is done at different cases and presented its dynamics in the form of simulation more clearly. The effects of delay are analyzed through the use of mathematical and numerical tools. Analytical analysis of direction of hopf bifurcation is presented well. Finally computer simulation is carried for different delay values and for different parameter values also. Numerical analysis of the model is also conducted to determine the impact of certain critical parameters on the disease’s course and presented with remarkable observations.